Exploring finite density QCD phase transition with canonical approach - Power of multiple precision computation -

Abstract

The canonical approach for finite density lattice QCD has a numerical instability. This instability makes it difficult to use the method reliably at the finite real chemical potential region. We studied this instability in detail and found that it is caused by the cancellation of significant digits. In order to reduce the effect of this cancellation, we adopt the multiple precision calculation for our discrete Fourier transformation (DFT) program, and we get the canonical partition function Z C (n, T ) with required accuracy. From the obtained Z C (n, T ), we calculate Lee-Yang zero distribution varying the number of significant digits. As a result, some curves surround the origin in the fugacity plane, but they are moved by varying the number of significant digits. Hence, we conclude that these curves are pseudo phase transition lines, and not real ones.

Canonical approach -- Investigation of finite density QCD phase transition

“…This figure was already published in Ref. [45] that, for temperatures above and below T c , the results are reliable up to µ B /T = 4 and µ B /T = 3-3.5, respectively. However, near T c , the reliable chemical potential range are limited up to µ B /T = 2.4.…”

“…This figure was already published in Ref. [45] signals of the finite density transition between the confinement-deconfinement phases is not observed yet in this case.…”

“…The data points plotted in the additional colors of dark red, dark green, dark blue, dark cyan, dark magenta, and dark brown points are the results at T /T c = 1.35(7), 1.20(6), 1.08(5), 0.99(5), 0.93(5) and 0.84(4), respectively, as calculated by the MPR method. This figure was already published in Ref [45].…”

“…We do not understand yet why Z C (n) is saturated at n = 50. Although it had not been investigated for a long time, the author studied it from a numerical standpoint recently [45,46]. First, the author considered that this saturation is caused by the numerical errors, and if we understand how the errors affect to our calculation, we can reduce this saturation.…”

“…First, the author considered that this saturation is caused by the numerical errors, and if we understand how the errors affect to our calculation, we can reduce this saturation. He notes that we can classify the numerical errors into four types of errors [45] (see also Refs. [47] and [48]).…”